Powerful Sunglasses

This is a puzzle.

Imagine I own a pair of sunglasses that reliably blocks ultraviolet rays so that, out of any ten rays that shine on it, only one of them gets through.  So, if 40 rays shine on them, only 4 make it through.  (And we’ll assume here that this is true across the whole spectrum, which won’t hold in reality).  These glasses we’ll call power 10 glasses.


I also own a pair of power 20 glasses: to get one ray through, 20 rays need to shine on it.  I’m thinking that sometimes I’ll need more protection, maybe power 100.  I check the following price list:

\begin{matrix} power & dollars \\ \hline \\ 10 & 20.00 \\ 20 & 30.00 \\ 30 & 40.00 \end{matrix}

and figure I can extrapolate the price for power 100.  But that sounds steep to me, especially for occasional use.

How much would it cost?  Do I really need to pay that much?

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